Late Professor Yanai has contributed to many fields ranging from aptitude diagnostics, epidemiology, and nursing to psychometrics and statistics. This paper reviews some of his accomplishments in linear algebra and multivariate analysis through his collaborative work with the present author, along with some untold episodes for the inception of key ideas underlying the work. The various topics covered include constrained principal component analysis, extensions of Khatri’s lemma, the Wedderburn-Guttman theorem, ridge operators, decompositions of the total association between two sets of variables, and ideal instruments. A common thread running through all of them is projectors and singular value decomposition (SVD), which are the main subject matters of a recent monograph by Yanai, Takeuchi, and Takane (2011).
